Journal of Applied Mathematics

Journal of Applied Mathematics / 2003 / Article

Open Access

Volume 2003 |Article ID 503451 | https://doi.org/10.1155/S1110757X03301147

Shabbir Ahmed, Charles Collins, "Variational analysis for simulating free-surface flows in a porous medium", Journal of Applied Mathematics, vol. 2003, Article ID 503451, 20 pages, 2003. https://doi.org/10.1155/S1110757X03301147

Variational analysis for simulating free-surface flows in a porous medium

Received29 Jan 2003
Revised25 Mar 2003

Abstract

A variational formulation has been developed to solve a parabolic partial differential equation describing free-surface flows in a porous medium. The variational finite element method is used to obtain a discrete form of equations for a two-dimensional domain. The matrix characteristics and the stability criteria have been investigated to develop a stable numerical algorithm for solving the governing equation. A computer programme has been written to solve a symmetric positive definite system obtained from the variational finite element analysis. The system of equations is solved using the conjugate gradient method. The solution generates time-varying hydraulic heads in the subsurface. The interfacing free surface between the unsaturated and saturated zones in the variably saturated domain is located, based on the computed hydraulic heads. Example problems are investigated. The finite element solutions are compared with the exact solutions for the example problems. The numerical characteristics of the finite element solution method are also investigated using the example problems.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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